Final answer:
In a regular hexagon where AB has a bearing of N 25° E, by adding 60° to each consecutive side's bearing in a clockwise direction, we find that the bearing of line FA is N 55° W.
Step-by-step explanation:
The question involves a regular hexagon with sides AB, BC, CD, DE, EF, and FA, and a given bearing of line AB which is N 25° E. We are asked to find the bearing of line FA. Since ABCDEF is a regular hexagon, each interior angle is 120°. When moving clockwise around a regular hexagon, each exterior angle is 60°, which is the turning angle from one side to the next.
The bearing of line AB is N 25° E, so every consecutive clockwise bearing can be found by adding 60° to the previous one, while keeping in mind that full rotation is 360°. Consequently, in clockwise order starting with line AB:
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- AB is N 25° E
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- BC is N 85° E (25° + 60°)
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- CD is S 5° E (85° + 60°, flipping from north to south because it exceeds 90°)
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- DE is S 65° E (5° + 60°)
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- EF is S 125° E (65° + 60°, but since it exceeds 90°, we switch to measuring from south)
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- FA would then be N 55° W (180° - 125° to find the complementary bearing, and flipping east to west because we are passing back from south to north)
Therefore, the bearing of line FA is N 55° W.